Internal problem ID [13152]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x^{2}+3 y x=6 \,{\mathrm e}^{-x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x)+3*x*y(x)=6*exp(-x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-3 \,{\mathrm e}^{-x^{2}}+c_{1}}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 21
DSolve[x^2*y'[x]+3*x*y[x]==6*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-3 e^{-x^2}+c_1}{x^3} \]